We study a nonlinear Dirac system in one space dimension with a quadratic nonlinearity which exhibits null structure in the sense of Klainerman. Using an L-p variant of the L-2 restriction method of Bourgain and Klainerman-Machedon, we prove local well-posedness for initial data in a Sobolev-like space (H-s,H-p) over cap (R) whose scaling dimension is arbitrarily close to the critical scaling dimension.
|Number of pages||12|
|Journal||Discrete and Continuous Dynamical Systems - Series A|
|Publication status||Published - Mar 2008|